Explore topic-wise InterviewSolutions in Current Affairs.

Out of 10 persons sitting at a round table. Three persons are selected at random one after the other. The chance that no two of the selected are together.

For real numbers x and y, we write $xRy\iff x-y+\sqrt{2}$ is an irrational number. Then the relation R is

The domain of $y=si{n}^{-1}(1+3x+2x^2)$ is:

The third derivative of a function f(x) vanishes for all x. If f(0)=1, f'1(1)=2 and f”(1) = – 1, then f(x) is equal to

If $a\in R$ and the equation $-3(x-[x]{)}^2+2(x-\left[x\right])+a^2=0$ $($where $\left[x\right]$ dentotes the greatest integer $\le x)$ has no integral solution, then all possible values of $a$ lie in the interval:

Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basket ball, 15 play hockey and basket ball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all ?

The term independent of $x$ in the product $(4+x+7x^2)(x-\frac{3}{x}{)}^{11}$ is

If a is any real number,the number of roots of cot x =a in the first quadrant is (are).

A railway train is travelling on a circular curve of $1500$ metres radius at the rate of $66km/hr$. Through what angle has it turned in $10$ seconds?

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus-rectum.

The line $\frac{x}{a}+\frac{y}{b}=1$ touches the curve $y=b{e}^{\frac{x}{a}}$ at the point

The solution of differential equation $x\frac{dy}{dx}+2y=x^2$ is......

The product 32, $\left(32{)}^{\frac{1}{6}}\right(32{)}^{\frac{1}{36}}$ ....... to $\infty$ is equal to

The differential equation representing the family of curves y = mx, where m is arbitrary constant, is

The vertices $B$ and $C$ of a $△ABC$ lie on the line, $\frac{x+2}{3}=\frac{y-1}{0}=\frac{z}{4}$ such that $BC=5$ units. Then the area (in sq. units) of this triangle, given that the point $A(1,-1,2)$, is :

If a, b, c are in G.P., prove that the following are also in G.P. :

(i) $a^2,b^2,c^2$

(ii) $a^3,b^3,c^3$

(iii) $a^2+b^2,ab+bc,b^2+c^2$

Read the following.


Then $K_{eq}=?$

If $\overrightarrow{a},\overrightarrow{b}$ are unit vectors such that the vector $\overrightarrow{a}+3\overrightarrow{b}$ is perpendicular to $7\overrightarrow{a}-5\overrightarrow{b}$ and $\overrightarrow{a}-4\overrightarrow{b}$ is perpendicular to $7\overrightarrow{a}-2\overrightarrow{b}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Choose the correct answer
The area of the circle $x^2+y^2=16$ exterior to the parabola $y^2=6x$ is
(a) $\frac{4}{3}(4\pi -\sqrt{3})$ (b) $\frac{4}{3}(4\pi +\sqrt{3})$
(c) $\frac{4}{3}(8\pi -\sqrt{3})$ (d) $\frac{4}{3}(8\pi +\sqrt{3})$

The value of $\underset{0}{\overset{2\pi }{\int }}\left[\sin 2x\right(1+\cos 3x\left)\right]dx$, where $\left[t\right]$ denotes the greatest integer function, is :

If $\omega$ is a cube root of unity, then $\omega$ + ${\omega }^{(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\frac{27}{128}+...........\infty )}$ =

If $\int f\left(x\right)dx=F\left(x\right)$, then $\int f\left(5x\right)dx$=

(i) If $tanA=\frac{5}{6}$ and $tanB=\frac{1}{11},$ prove that A+B= $\frac{\pi }{4}$
(ii) If $tanA=\frac{m}{m-1}$ and $tanB=\frac{m}{2m-1}$
then prove that $A-B=\frac{\pi }{4}$

Let $x_1,x_2,x_3,x_4$ be four non-zero numbers satisfying the equation $ta{n}^{-1}\left(\frac{a}{x}\right)+ta{n}^{-1}\left(\frac{b}{x}\right)+ta{n}^{-1}\left(\frac{c}{x}\right)+ta{n}^{-1}\left(\frac{d}{x}\right)=\frac{\pi }{2},$ then which of the following relation hold(s) good?

A plane bisects the line segment joining the points $(1,2,3)$ and $(-3,4,5)$ at right angles. Then this plane also passes through the point :

The Fibonacci sequence is defined by $a_1=1,a_2,a_n=a_{n-1}+a_{n-2}$ for n > 2. Find $\frac{a_{n+1}}{a_n}$ for n = 1, 2, 3, 4, 5.

Let A(0, 6, 6), B(6,6, 0) and C(6, 0, 6) are three points and the point D is moving on the line x + z - 3 = 0 = y. If G is centroid of $\Delta ABC$, then minimum value of GD is ___

Find the solution of differential equation
$\frac{dy}{dx}=\frac{(\sin y+e^x)}{(\ln y-x\cos y)}$ is

Which of the following lines have the intercepts of equal lengths made by the circle $x^2+y^2-2x+4y=0$ is/are

${lim}_{x\to 0}\frac{x^{3}cotx}{1-cosx}$

The number of integers in the range of $f\left(x\right)={\sec }^{-1}(9x^2+6x-1)$ is

If the cartesian coordinates of a point are $(\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}),$ then the polar coordinates are

The circle $x^2+y^2-4x-4y+4=0$ is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is $x+y-xy+k\sqrt{x^2+y^2}=0$, then the value of $k$ is equal to

Integrate the function.
$\int \sqrt{x^2+3x}dx$

If A ={1,2,3,4}, define relations on A which have properties of being
(ii)symmetric but neither reflexive nor transitive.

The length of the sub-tangent and sub-normal is equal for the curve $y=e^{\mathrm{px}}+\mathrm{px}$ at the point (0, 1), then the value of p is

If $\sin x+\cos x=y^2-y+a$ has no value of $x$ for any value of $y$ then $a$ belongs to

The number of ways in which $100$ people can be divided in $50$ pairs is